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Bayesian Estimation and Model Choice in Item Response Models

Sahu, Sujit K. (2002) Bayesian Estimation and Model Choice in Item Response Models Journal of Statistical Computation and Simulation, 72, (3), pp. 217-232. (doi:10.1080/00949650212387).

Record type: Article


Item response models are essential tools for analyzing results from many educational and psychological tests. Such models are used to quantify the probability of correct response as a function of unobserved examinee ability and other parameters explaining the difficulty and the discriminatory power of the questions in the test. Some of these models also incorporate a threshold parameter for the probability of the correct response to account for the effect of guessing the correct answer in multiple choice type tests.
In this article we consider fitting of such models using the Gibbs sampler. A data augmentation method to analyze a normal-ogive model incorporating a threshold guessing parameter is introduced and compared with a Metropolis-Hastings sampling method. The proposed method is an order of magnitude more efficient than the existing method. Another objective of this paper is to develop Bayesian model choice techniques for model discrimination. A predictive approach based on a variant of the Bayes factor is used and compared with another decision theoretic method which minimizes an expected loss function on the predictive space. A classical model choice technique based on a modified likelihood ratio test statistic is shown as one component of the second criterion. As a consequence the Bayesian methods proposed in this paper are contrasted with the classical approach based on the likelihood ratio test. Several examples are given to illustrate the methods.

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Submitted date: 2002
Keywords: data augmentation, Gibbs sampler, Markov chain Monte Carlo, model choice, likelihood ratio statistic, predictive distribution, three parameter Model
Organisations: Statistics


Local EPrints ID: 38459
ISSN: 0094-9655
PURE UUID: 9629339e-d7f4-4e5a-a714-3b4e4f58e1ca
ORCID for Sujit K. Sahu: ORCID iD

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Date deposited: 09 Jun 2006
Last modified: 17 Jul 2017 15:38

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